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A092936
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Area of n-th triple of hexagons around a triangle.
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4
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1, 9, 100, 1089, 11881, 129600, 1413721, 15421329, 168220900, 1835008569, 20016873361, 218350598400, 2381839709041, 25981886201049, 283418908502500, 3091626107326449, 33724468272088441, 367877524885646400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is the unsigned member r=-9 of the family of Chebyshev sequences S_r(n) defined in A092184: ((-1)^(n+1))*a(n) = S_{-9}(n), n>=0.
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FORMULA
| a(n)=10*(a(n-1)+a(n-2))-a(n-3), a(1)=1, a(2)=9, a(3)=100. G.f.: (1-x)*x/(1-10*x-10*x^2+x^3). a(n)=((3-Sqrt(13))^n-(3+Sqrt(13))^n)^2/(13*4^n)
a(n)= 2*(T(n, 11/2)-(-1)^n)/13 with twice the Chebyshev's polynomials of the first kind evaluated at x=11/2: 2*T(n, 11/2)=A057076(n)=((11+3*sqrt(13))^n + (11-3*sqrt(13))^n)/2^n. W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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EXAMPLE
| a(5)=10*(1089+100)-9=11881. From A006190, a(5)=(3*33+10)^2=11881
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MAPLE
| seq(fibonacci(n, 3)^2, n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2008
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MATHEMATICA
| CoefficientList[Series[(1-x)*x/(1-10*x-10*x^2+x^3), {x, 0, 20}], x] (CoefficientList[Series[x/(1-3*x-x^2), {x, 0, 20}], x])^2 Table[Round[((3+Sqrt[13])^n)^2/(13*4^n)], {n, 1, 20}]
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CROSSREFS
| Equals (A006190)^2
Cf. A005386, A006190.
Sequence in context: A017018 A027769 A065736 * A056002 A060150 A202833
Adjacent sequences: A092933 A092934 A092935 * A092937 A092938 A092939
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KEYWORD
| easy,nonn
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AUTHOR
| Peter J. C. Moses. (mows(AT)mopar.freeserve.co.uk), Apr 18 2004
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